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Barycentric Straightening, Splitting Rank and Bounded Cohomology
Wang, Shi

2016, Doctor of Philosophy, Ohio State University, Mathematics.
This work is devoted to the study of bounded cohomology from a geometric point of view. In the context of non-compact, connected, semisimple Lie groups with finite center, Dupont raised the question of whether the comparison map is always surjective. The main goal of this work is to show Dupont's conjecture in high degrees. We introduce the barycentric straightening and show that the straightened simplices in higher rank symmetric spaces of non-compact type has uniformly bounded volume, when the dimension of the simplices are close to the dimension of the symmetric spaces. We also give counterexamples where the barycentrically straightened simplices have unbounded volume when the dimension is equal to the splitting rank. This provides an obstruction to our straightening method. In addition, we compute explicitly this splitting rank for all symmetric spaces.
Jean Lafont (Advisor)
Michael Davis (Committee Member)
James Fowler (Committee Member)
82 p.

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Wang, S. (2016). Barycentric Straightening, Splitting Rank and Bounded Cohomology. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Wang, Shi. "Barycentric Straightening, Splitting Rank and Bounded Cohomology." Electronic Thesis or Dissertation. Ohio State University, 2016. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Wang, Shi "Barycentric Straightening, Splitting Rank and Bounded Cohomology." Electronic Thesis or Dissertation. Ohio State University, 2016. https://etd.ohiolink.edu/

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